The electrostatic problem for a homogeneous axisymmetric particle is considered. The approach applied is similar to the
extended boundary condition method often used in the light scattering theory. The surface integrals forming the elements
of an analog of the well known T–matrix are studied in detail. The inverse problem is solved under the condition that the
internal field is uniform. It is proved that this condition is satisfied for axisymmetric particles only if they are spheroids.
Approximate solutions to the electrostatic problem that are based on the assumption of the uniform internal field are
discussed as well.
We suggest a separation of variables method based on expansions of the electromagnetic fields in terms of spheroidal wave
functions. Our approach includes splitting the fields in two specific parts and choice of proper scalar potentials for each
of them. An earlier analysis of similar methods in the case of a spherical basis has shown that the SVM has a wider
practical applicability range than other methods. It was also found that when using a spheroidal basis our general approach
gave reliable results for particles of high eccentricity for which other approaches were inapplicable. Thus, the suggested
SVM should be highly efficient in calculations of optical properties of various nonspherical scatterers in a wide range of
There are many exact theoretical methods to simulate light scattering by small particles, but only a few of them, including in the first turn the Extended Boundary Condition Method (EBCM), allow one to perform calculations usually required in practical tasks, i.e. to take into account size, orientation and so on distributions of (simple model) scatterers. Importance of these methods caused by their wide applications was stimulating long time investigations of their applicability ranges. We report recent results of the analysis of EBCM-like methods. It is confirmed that the methods give a convergent solution (i.e. are mathematically correct) everywhere under the known conditions of validity of the Rayleigh hypothesis. Convergence of these methods used to calculate only the far-field characteristics of the scattered field (cross-sections, scattering matrix, etc.) occurs under a weaker condition. These general conditions are applied to the particular cases of spheroidal and Chebyshev particles as well as particles with sharp edges, and numerical results confirming the conclusions of our theoretical analysis are presented.
Real scatterers are known to usually have complex shape and some structure. Therefore, to perform light scattering simulations, one should specify their models and select proper computational methods. To help in solution of these problems, we have created an internet cite DOP (Database of Optical Properties of non-spherical particles). The currnet content of the DOP (optical constants, reviews and bibliographies, codes, etc.) is briefly described. A special attention is paid to recently developed fast methods and codes to treat light scattering by non-spherical inhomogeneous particles using the layered models. First results of application of these tools to comparable study of the optical properties of layered particles and particles with inclusions are presented.
The new solution of the problem of light scattering by coated spheroids was used to calculate the optical properties of prolate and oblate particles. The solution was obtained by the method of separation of variables for confocal spheroids. We consider the silicate core ice mantle particles and present the extinction cross-sections for prolate and oblate spheroids with the refractive indices m<SUB>core</SUB> equals 1.7 + Oi, 1.7 + 0.1i and m<SUB>mantle</SUB> equals 1.3, the aspect ratio (a/b)<SUB>mantle</SUB> equals 2 and various volume ratios V<SUB>core</SUB>/V<SUB>total</SUB>. The results are plotted for different size parameters x<SUB>v</SUB> equals 2(pi) r<SUB>v</SUB>/(lambda) , where r<SUB>v</SUB> is the radius of equivolume sphere and (lambda) is the wavelength of incident radiation. The main conclusions are: (a) if V<SUB>core</SUB>/V<SUB>total</SUB> equals 0.5, the optical properties of a core-mantle particle are determined mainly by its core: for prolate non-absorbing spheroids when x<SUB>v</SUB> <EQ 4.5; for prolate absorbing spheroids when x<SUB>v</SUB> <EQ 4.5 or x<SUB>v</SUB> > 10, for oblate absorbing and non-absorbing spheroids when x<SUB>v</SUB> <EQ 10. (b) the linear growth of the extinction cross-sections on the volume ratio V<SUB>core</SUB>/V<SUB>total</SUB> is obtained for prolate particles with x<SUB>v</SUB> equals 1 and 2. (c) the non-linear increase of cross- sections is obtained for oblate particles with size parameters x<SUB>v</SUB> equals 1 - 5. (d) the small imaginary part of the core refractive index m [Im(m) < 0.01] practically does not change the optical properties of an inhomogeneous particle. When the imaginary part reaches 0.1, the noticeable changes of cross-sections may be detected.
The solution of the electromagnetic scattering problem for cofocal coated spheroids obtained by the method of separation of variables in a spheroidal coordinate system is presented. The main features of the scheme of the solution are: (a) the incident, scattered and internal fields are divided into two parts: the axisymmetric part which does not depend on the azimuthal angle and the non-axisymmetric one; the diffraction problem is solved independently for each part; (b) the scalar potentials for the solution of each problem are chosen by a special way: the Abraham's potentials (for the axisymmetric part) and superposition of the potentials used for spheres and cylinders (for the non-axisymmetric part). Then, we derive the systems of linear algebraic equations in the simplest form and can investigate them analytically. Such a scheme allows to solve the light scattering problem for spheroids with arbitrary asphericity and has an advantage in comparison with other approaches, especially for large values of the aspect ratio: the computational time is being reduced in about ten times for small values of the aspect ratio (a/b equals 2) and in about hundred times for a/b equals 10 in comparison with the well-known solution of Asano and Yamamoto.